Superstatistics and canonical quantization of the damped harmonic oscillator

2019 ◽  
Vol 34 (14) ◽  
pp. 1950108 ◽  
Author(s):  
S. Sargolzaeipor ◽  
H. Hassanabadi ◽  
W. S. Chung
Keyword(s):  
Thermodynamic Properties ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Canonical Quantization ◽  
Quantization Method ◽  
Dirac Delta ◽  
Energy Eigenvalues ◽  
Damped Harmonic Oscillator ◽  
Gamma Distributions

In this paper, we investigate the behavior of the energy eigenvalues of the Schrödinger equation by using the canonical quantization method. We obtain the Hamiltonian of the Schrödinger equation by the Lagrangian in terms of the new coordinates. Then we calculate the partition function by the eigenvalues and the thermodynamic properties of the system in the superstatistics formalism for the modified Dirac delta and the Gamma distributions. All results in the limiting cases satisfy that of the harmonic oscillator. Furthermore, the effects of the all parameters in the problem of energy eigenvalues and thermodynamic properties are calculated and shown graphically.

Superstatistics of two electrons quantum dot

2019 ◽  
Vol 34 (03) ◽  
pp. 1950023 ◽  
Author(s):  
S. Sargolzaeipor ◽  
H. Hassanabadi ◽  
W. S. Chung
Keyword(s):  
Energy Spectrum ◽  
Thermodynamic Properties ◽  
Quantum Dot ◽  
Schrödinger Equation ◽  
Analytical Method ◽  
Schrodinger Equation ◽  
Boltzmann Factor ◽  
Dirac Delta ◽  
Uniform Distributions ◽  
Parabolic Quantum Dot

In this paper, we discussed the Schrödinger equation in the presence of the harmonic two electrons interaction for the parabolic quantum dot and the energy spectrum by an analytical method is obtained, then the effective Boltzmann factor in a deformed formalism for modified Dirac delta and uniform distributions are derived. We make use of the superstatistics for the two distributions in physics and the thermodynamic properties of the system are calculated. Ordinary results are recovered for the vanishing deformed parameter. Furthermore, the effect of all parameters in the problems are calculated and shown graphically.

scholarly journals Quantization of the one-dimensional free harmonic oscillator as an example of the application of the node theorem and the Macdonald-Hylleraas-Undheim theorem

2020 ◽  
Vol 22 (1) ◽  
pp. 87-90
Author(s):  
Kunle Adegoke ◽  
A. Olatinwo
Keyword(s):  
Differential Equation ◽  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Hermite Polynomials ◽  
Traditional Methods ◽  
One Dimensional ◽  
Energy Eigenvalues ◽  
The One

Using heuristic arguments alone, based on the properties of the  wavefunctions, the energy eigenvalues and the corresponding eigenfunctions of the one-dimensional harmonic oscillator are obtained. This approach is considerably simpler and is perhaps more intuitive than the traditional methods of solving a differential equation and manipulating operators. Keywords: Time-independent Schrödinger equation, MacDonald-Hylleraas-Undheim theorem, Node theorem, Hermite polynomials,  energy eigenvalues

The investigation of Carnot engine in the presence of deformed formalism

2021 ◽  
Vol 36 (35) ◽  
Author(s):  
H. Naseri Karimvand ◽  
B. Lari ◽  
H. Hassanabadi ◽  
W. S. Chung
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Thermodynamic Properties ◽  
Schrödinger Equation ◽  
Single Particle ◽  
Schrodinger Equation ◽  
Carnot Cycle ◽  
Energy Eigenvalues ◽  
Work Done

In this paper, after introducing a kind of [Formula: see text]-deformation in quantum mechanics, first [Formula: see text]-deformed form of Schrödinger equation for a single particle in a box is derived. Then, the energy eigenvalues and wave function in Schrödinger equation are studied. Also, we discuss the Carnot cycle by using of the energy eigenvalues. We obtain the thermodynamic properties such as force, heat transferred, work done and efficiency in the cycle. Finally, all results have satisfied what we had expected before.

scholarly journals Q-Deformed Morse and Oscillator Potential

2017 ◽  
Vol 2017 ◽  
pp. 1-4 ◽  
Author(s):  
H. Hassanabadi ◽  
W. S. Chung ◽  
S. Zare ◽  
S. B. Bhardwaj
Keyword(s):  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Schrodinger Equation ◽  
Analytic Solutions ◽  
Wave Functions ◽  
Oscillator Potential ◽  
Energy Eigenvalues

We studied the q-deformed Morse and harmonic oscillator systems with appropriate canonical commutation algebra. The analytic solutions for eigenfunctions and energy eigenvalues are worked out using time-independent Schrödinger equation and it is also noted that these wave functions are sensitive to variation in the parameters involved.

Nonrelativistic Solutions of Schrodinger Equation and Thermodynamic Properties with the Proposed Modified Mobius Square Plus Eckart Potential

2021 ◽  
Author(s):  
Chibueze P. Onyenegecha ◽  
Ifeanyi J. Njoku ◽  
Alex I. Opara ◽  
Obi Kingsley Echendu ◽  
Ejiro N. Omokoro ◽  
...  
Keyword(s):  
Thermodynamic Properties ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Eckart Potential

scholarly journals Dirac’s Method for the Two-Dimensional Damped Harmonic Oscillator in the Extended Phase Space

Mathematics ◽  
2018 ◽  
Vol 6 (10) ◽  
pp. 180 ◽  
Author(s):  
Laure Gouba
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Canonical Quantization ◽  
Extended Phase Space ◽  
Two Dimensional ◽  
Class Constraint ◽  
Extended Phase ◽  
Damped Harmonic Oscillator ◽  
Points Of View ◽  
Space Description

The system of a two-dimensional damped harmonic oscillator is revisited in the extended phase space. It is an old problem that has already been addressed by many authors that we present here with some fresh points of view and carry on a whole discussion. We show that the system is singular. The classical Hamiltonian is proportional to the first-class constraint. We pursue with the Dirac’s canonical quantization procedure by fixing the gauge and provide a reduced phase space description of the system. As a result, the quantum system is simply modeled by the original quantum Hamiltonian.

scholarly journals Time-covariant Schrödinger equation and invariant decay probability: the $$\Lambda $$-Kantowski–Sachs universe

2021 ◽  
Vol 81 (12) ◽  
Author(s):  
Theodoros Pailas ◽  
Nikolaos Dimakis ◽  
Petros A. Terzis ◽  
Theodosios Christodoulakis
Keyword(s):  
Schrödinger Equation ◽  
Wave Packet ◽  
Time Dependence ◽  
Schrodinger Equation ◽  
Canonical Quantization ◽  
Dynamical Equations ◽  
Quadratic Constraint ◽  
Decay Probability ◽  
Flrw Universe ◽  
Arbitrary Time Dependence

AbstractThe system under study is the $$\Lambda $$ Λ -Kantowski–Sachs universe. Its canonical quantization is provided based on a recently developed method: the singular minisuperspace Lagrangian describing the system, is reduced to a regular (by inserting into the dynamical equations the lapse dictated by the quadratic constraint) possessing an explicit (though arbitrary) time dependence; thus a time-covariant Schrödinger equation arises. Additionally, an invariant (under transformations $$t=f({\tilde{t}})$$ t = f ( t ~ ) ) decay probability is defined and thus “observers” which correspond to different gauge choices obtain, by default, the same results. The time of decay for a Gaussian wave packet localized around the point $$a=0$$ a = 0 (where a the radial scale factor) is calculated to be of the order $$\sim 10^{-42}{-}10^{-41}~\text {s}$$ ∼ 10 - 42 - 10 - 41 s . The acquired value is near the end of the Planck era (when comparing to a FLRW universe), during which the quantum effects are most prominent. Some of the results are compared to those obtained by following the well known canonical quantization of cosmological systems, i.e. the solutions of the Wheeler–DeWitt equation.

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